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Teaching materials I used for John's topology class on 9/6/2018
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README.md

Lecture on 0D Persistent Homology

This notebook is meant to cover the basics of lower star filtrations, with a focus on 0D homology. It covers the following topics

  • 0D point cloud filtrations
  • 1D Time Series Lower Star Filtrations
  • Lower star on images
  • Lower star on 3D shapes
  • Merge Trees

Directions are below for installing the code. Please e-mail chris.tralie@gmail.com if you encounter any issues.

Installing Jupyter Notebook And Other Dependencies

To run these modules, you will need to have jupyter notebook installed with a Python 3 backend with numpy, scipy, and matplotlib. If you don't have this on your computer yet, the easiest way to install this is with Anaconda:

https://www.anaconda.com/download/

Once you have downloaded and installed all of these packages, type the following commands in the terminal, which will install dependencies

pip install cython
pip install ripser

Running the code

First, check out the code from github

git clone --recursive https://github.com/ctralie/Homology0D_Teaching.git
cd Homolgy0D_Teaching

At the root of this directory, type

jupyter notebook

This will launch a browser window, where you can run the modules. Click on ConnectedComponentsLecture.ipynb. If you want to see the solutions we went through in class, click on ConnectedComponentsLecture_Completed.ipynb.

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